I’m not going to call these the best papers, or the most cited (although some of them are), but they all contain things that were interesting or unique that encouraged further work and discussion (even if myself and others disagreed with the results) and thus, they got gingerbread cookies baked in their honour. So without further ado, these are the 10 cookies highlights from 2010 literature in general relativity, quantum gravity, and gravitation (ranked by date of e-print, so don’t read into the order):

## Thermodynamics of *Hořava*-Lifshitz black holes

Yun Soo Myung, & Yong-Wan Kim (2010). Thermodynamics of *Hořava*-Lifshitz black holes. Eur.Phys.J. C68 (2010) 265-270 arXiv: 0905.0179v3

### The abstract:

We study black holes in the Ho*ř*ava-Lifshitz gravity with a parameter λ. For 1/3≤ λ < 3, the black holes behave the Lifshitz black holes with dynamical exponent 0 < z ≤ 4, while for λ > 3, the black holes behave the Reissner-Nordstr¨om type black hole in asymptotically flat spacetimes. Hence, these all are quite different from the Schwarzschild-AdS black hole of Einstein gravity. The temperature, mass, entropy, and heat capacity are derived for investigating thermodynamic properties of these black holes.

### The cookies:

Using this first law [of thermodynamics], we derive an entropy…

Equation 28

### Why this paper?

So, obviously a *Hořava*-Lifshitz gravity paper was a must for 2010, but selecting which one was difficult. While this paper was technically written in 2009, it was baked published in the *European Physical Journal* in 2010 (and it was in 2010 that it was really being discussed). Cited, approximately 95 times, it’s clearly on the more delicious side of *Hořava*-Lifshitz.

## String Axiverse

Asimina Arvanitaki, Savas Dimopoulos, Sergei Dubovsky, Nemanja Kaloper, & John March-Russell (2009). String Axiverse Phys.Rev. D, 81 arXiv: 0905.4720v2

### The abstract:

String theory suggests the simultaneous presence of many ultralight axions possibly populating each decade of mass down to the Hubble scale 10⁻³³eV. Conversely the presence of such a plenitude of axions (an ‘axiverse’) would be evidence for string theory, since it arises due to the topological complexity of the extra-dimensional manifold and is ad hoc in a theory with just the four familiar dimensions. We investigate how upcoming astrophysical experiments will explore the existence of such axions over a vast mass range… The rapidly rotating black hole in the X-ray binary LMC X-1 implies an upper limit on the decay constant of the QCD axion fₐ ≤ 2 x 10¹⁷ GeV, much below the Planck mass…

### The cookies:

###

Figure 6: The Carnot Cycle of the Axionic Instability: The black hole "feeds" the superradiant state forming an axion Bose-Einstein condensate. Axions from that state quantummechanically transition through graviton emission to a lower-energy non-superradiant state. The non-superradiant state decays into the black hole. Accreting matter around the black hole replenishes the rotational energy lost to gravitons and sustains this cycle.

### Why this paper?

Testing stringy ideas with astrophysics! At 42 pages and a respectable 35 citations, I choose this paper as one of the most enjoyable from 2010 because it presents a fairly abstract idea with a clever way to test it. One of the hardest tasks in theoretical physics, especially in quantum gravity, is to figure out recipes observations that would uniquely confirm your ideas, and that’s basically what this team has done.

## On the Origin of Gravity and the Laws of Newton

Erik P. Verlinde (2010). On the Origin of Gravity and the Laws of Newton arXiv arXiv: 1001.0785v1

### The abstract:

Starting from first principles and general assumptions Newton’s law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton’s law of inertia needs to be explained. The equivalence principle leads us to conclude that it is actually this law of inertia whose origin is entropic.

### The cookies:

When a particle has an entropic reason to be on one side of the membrane and the membrane carries a temperature, it will experience an eeffective force equal to

Equation 3.7

This is the entropic force.

### Why this paper?

I’m sure some can guess how it pains me to bake this one, but Verlinde certainly got a lot of people talking about new ideas, and spawned a lot of publications by other researchers in 2010 (132 citations and counting). For that unsatisfied taste left in your mouth after the above, try Padmanabhan’s “Surface Density of Spacetime Degrees of Freedom from Equipartition Law in theories of Gravity” 1003.5665v2.

## Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation

E. Komatsu, et al. (2010). Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation arXiv arXiv: 1001.4538v3 (see also: *There Cosmic Microwave Background Anomalies?* 1001.4758v1)

### The abstract:

The 7-year WMAP data and improved astrophysical data rigorously test the standard cosmological model and its extensions. By combining WMAP with the latest distance measurements from BAO and H0 measurement, we determine the parameters of the simplest LCDM model. …

### The cookies:

Fig. 7.— The WMAP 7-year temperature power spectrum (Larson et al. 2010), along with the temperature power spectra from the ACBAR (Reichardt et al. 2009) and QUaD (Brown et al. 2009) experiments. We show the ACBAR and QUaD data only at l ≥ 690, where the errors in the WMAP power spectrum are dominated by noise. We do not use the power spectrum at l > 2000 because of a potential contribution from the SZ effect and point sources. The solid line shows the best-fitting 6-parameter flat CDM model to the WMAP data alone (see the 3rd column of Table 1 for the maximum likelihood parameters).

### Why this paper?

Now while this is certainly on the observational side of things, seeing as it was the culmination of a huge experiment, profoundly critical to cosmology, it seemed well worth to include in a 2010 list (the 635 citations this year also suggest that). The prep. time was well worth the results here.

## Introduction to Holographic Superconductors

Gary T. Horowitz (2010). Introduction to Holographic Superconductors arXiv arXiv: 1002.1722v2

### The abstract:

These lectures give an introduction to the theory of holographic superconductors. These are superconductors that have a dual gravitational description using gauge/gravity duality. After introducing a suitable gravitational theory, we discuss its properties in various regimes: the probe limit, the effects of backreaction, the zero temperature limit, and the addition of magnetic fields. Using the gauge/gravity dictionary, these properties reproduce many of the standard features of superconductors. …

### The cookies:

The gauge/gravity dictionary says that the retarded Green’s function (for Jx) in the dual field theory is

Equation 60

### Why this paper?

So this one is a little different than the above, as it doesn’t really present a new result, but it is, in fact a mini lecture series on a hot new topic. Why did I choose this instead of one of the papers it cited, perhaps? Well, because Horowitz sets out the ingredients better than almost anybody else. In terms of clear pieces of literature written on the amazing beauty that is the AdS/CFT correspondence, this has got to be one of the best from 2010 (and it has been cited 64 times by those who hungrily agree).

## f(R) theories

Antonio De Felice, & Shinji Tsujikawa (2010). f(R) theories Living Rev. Rel. 13: 3, 2010 arXiv: 1002.4928v2

### The abstract:

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity – such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

### The cookies:

We start with the 4-dimensional action in f (R) gravity:

Equation 2.1

where κ² = 8πG, g is the determinant of the metric gμν, and LM is a matter Lagrangian1 that depends on gμν and matter fields ΨM.

### Why this paper?

Now this is another review paper (verging on “cook book”), but it is also a distinctly tasty one (cited 102 times so far). If you wanted *the* resource on f(R) theories of gravity, you’re in luck because it was written this year.

## Thermal time and the Tolman-Ehrenfest effect: temperature as the “speed of time”

Carlo Rovelli, & Matteo Smerlak (2010). Thermal time and the Tolman-Ehrenfest effect: temperature as the “speed of time” arXiv arXiv: 1005.2985v3

### The abstract:

The thermal time hypothesis has been introduced as a possible basis for a fully general-relativistic thermodynamics. Here we use the notion of thermal time to study thermal equilibrium on stationary spacetimes. Notably, we show that the Tolman-Ehrenfest effect (the variation of temperature in space so that Tgₒₒ⁻½ remains constant) can be reappraised as a manifestation of this fact: at thermal equilibrium, temperature is locally the rate of flow of thermal time with respect to proper time – pictorially, “the speed of (thermal) time”. Our derivation of the Tolman-Ehrenfest effect makes no reference to the physical mechanisms underlying thermalization, thus illustrating the import of the notion of thermal time.

### The cookies:

Given a statistical state ρ, we define the thermal time flow α : *A* → *A* as the Poisson flow of (−ln ρ) in *A*. That is

Equation 3

where the r.h.s. is the Poisson bracket.

### Why this paper?

Short and sweet (and currently only cited two times, not that that stops me from including it), Rovelli and Smerlak bring thermal time to stationary spacetimes. “Thermal time” is a catchy idea that is supposed to help general relativity and quantum mechanics blend with thermodynamics. Not only could these ideas be important for the unification of general relativity, quantum effects and thermodynamics, but they also play an important role in the *nature of time* debate. This is a paper that has serious rising potential.

## The Small Scale Structure of Spacetime

Steven Carlip (2010). The Small Scale Structure of Spacetime arXiv arXiv: 1009.1136v1

### The abstract:

Several lines of evidence hint that quantum gravity at very small distances may be effectively two-dimensional. I summarize the evidence for such “spontaneous dimensional reduction,” and suggest an additional argument coming from the strong-coupling limit of the Wheeler-DeWitt equation. If this description proves to be correct, it suggests a fascinating relationship between small-scale quantum spacetime and the behavior of cosmologies near an asymptotically silent singularity.

### The cookies:

For a scalar field, in particular, the propagator is determined by the heat kernel, and the behavior of the spectral dimension implies a structure

Equation 4

### Why this paper?

This is one of my favourites from the year; there is a lot of elegant physics contained within these pages (and yet still only two citations). Understanding the small scale structure of spacetime is going to be a major part of physics for the next few decades (at least), and coming at spontaneous dimensional reduction from CDT is a decent looking approach. Some of the delicious ideas discussed by Carlip may very well prove to be the base for our future understanding of a quantum spacetime.

## Black Hole Entropy, Loop Gravity, and Polymer Physics

Eugenio Bianchi (2010). Black Hole Entropy, Loop Gravity, and Polymer Physics arXiv arXiv: 1011.5628v1

### The abstract:

Loop Gravity provides a microscopic derivation of Black Hole entropy. In this paper, I show that the microstates counted admit a semiclassical description in terms of shapes of a tessellated horizon. The counting of microstates and the computation of the entropy can be done via a mapping to an equivalent statistical mechanical problem: the counting of conformations of a closed polymer chain. This correspondence suggests a number of intriguing relations between the thermodynamics of Black Holes and the physics of polymers.

### The cookies:

In particular, in the slowly rotating case, Smarr formula applies: the dependence of the entropy on the angular momentum is quadratic and given by

Equation 26

### Why this paper?

This was another paper that I really enjoyed recently; it’s hard not to find these correspondences staggeringly beautiful, honestly. While approaches combining polymer physics techniques with general relativity don’t have a big following yet, they’re definitely one of *the* growing ideas in LQG from 2010. Loop quantum gravity and polymer physics are just heating up the kitchen; we haven’t even see what they’ll really be making yet.

## Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity

V. G. Gurzadyan, & R. Penrose (2010). Concentric circles in WMAP data may provide evidence of violent pre-Big-Bang activity arXiv arXiv: 1011.3706

### The abstract:

Conformal cyclic cosmology (CCC) posits the existence of an aeon preceding our Big Bang ‘B’, whose conformal infinity ‘I’ is identified, conformally, with ‘B’, now regarded as a spacelike 3-surface. Black-hole encounters, within bound galactic clusters in that previous aeon, would have the observable effect, in our CMB sky, of families of concentric circles over which the temperature variance is anomalously low, the centre of each such family representing the point of ‘I’ at which the cluster converges. These centres appear as fairly randomly distributed fixed points in our CMB sky. The analysis of Wilkinson Microwave Background Probe’s (WMAP) cosmic microwave background 7-year maps does indeed reveal such concentric circles, of up to 6 σ significance. This is confirmed when the same analysis is applied to BOOMERanG98 data, eliminating the possibility of an instrumental cause for the effects. These observational predictions of CCC would not be easily explained within standard inflationary cosmology.

### The cookies:

Figure 1. Conformal diagram (without inflation) of the effect, according to CCC, of a pre-Big-Bang entity (a supermassive black-hole encounter, according to CCC which is the source of two violent events.

### Why this paper?

It’s everyone’s favourite topic this month: Penrose and Gurzadyan’s “evidence”* *for a cyclic cosmological model. Sure, they’re probably wrong, but come on, it’s Christmas! (expect the citation count to grow on this one steadily into the new year), plus, who doesn’t still get a little excited when Roger Penrose puts that apron on (*… wait… what?*).

_________________

Overarching themes: I did intentionally choose papers that were published on the arXiv (so they could be accessed from anywhere/by anyone), but that criteria didn’t actually affect my selections (as really, what from 2010 wasn’t on the arXiv?). Yes, yes, it was a little light on string theory topics, but that could very well be because more exciting things are happening elsewhere (or because I’m not all that stringy).

Note: Citation counts are only approximate and from the time that I am writing this post, of course.

And Another Note: The cookies start changing colour part way through because my second batch of dough was made with a different colour molasses. Also, the order they were made in correlates to how nice they look, as it was tiring.

Further Note: If any of the authors want their cookies… they’ll have probably been eaten already, but if you email me quickly, I’m willing to send them to you (or if you know me, just ask and I’ll make you some for whenever we’ll be running into each other next).