Scientific Series

In this talk I shall describe a general formalism based on $AdS_2/CFT_1$ correspondence that allows us to systematically calculate the entropy, index and other physical observables of an extremal black hole taking into account higher derivative and quantum corrections to the action. I shall also describe precise microscopic computation of the same quantities for a class of supersymmetric extremal black holes and compare this with the prediction of $AdS_2/CFT_1$ correspondence.

In this talk I shall describe a general formalism based on $AdS_2/CFT_1$ correspondence that allows us to systematically calculate the entropy, index and other physical observables of an extremal black hole taking into account higher derivative and quantum corrections to the action. I shall also describe precise microscopic computation of the same quantities for a class of supersymmetric extremal black holes and compare this with the prediction of $AdS_2/CFT_1$ correspondence.

In this talk I shall describe a general formalism based on $AdS_2/CFT_1$ correspondence that allows us to systematically calculate the entropy, index and other physical observables of an extremal black hole taking into account higher derivative and quantum corrections to the action. I shall also describe precise microscopic computation of the same quantities for a class of supersymmetric extremal black holes and compare this with the prediction of $AdS_2/CFT_1$ correspondence.

Using a formulation of the post-Newtonian expansion in terms of Feynman graphs, we discuss how various tests of General Relativity (GR) can be translated into measurement of the three- and four-graviton vertices. The timing of the Hulse-Taylor binary pulsar provides a bound on the deviation of the three-graviton vertex from the GR prediction at the 0.1% level. For coalescing binaries at interferometers, because of degeneracies with other parameters in the template such as mass and spin, the effects of modified three- and four-graviton vertices at the level of the restricted PN approximation, is to induce an error in the determination of these parameters and it is not possible to use coalescing binaries for constraining deviations of the vertices from the GR prediction.

Black holes play a central role in astrophysics and in physics more generally. Candidate black holes are nearly ubiquitous in nature. They are found in the cores of nearly all galaxies, and appear to have resided there since the earliest cosmic times. They are also found throughout the galactic disk as companions to massive stars. Though these objects are almost certainly black holes, their properties are not very well constrained. We know their masses (often with errors that are factors of a few), and we know that they are dense. In only a handful of cases do we have information about their spins. Gravitational-wave measurements will enable us to rectify this situation. Focusing largely on measurements with the planned space-based detector LISA, I will describe how gravitational-wave measurements will allow us to measure both the masses and spins of black holes with percent-level accuracy even to high redshift, allowing us to track their growth and evolution over cosmic time. I will also describe how a special class of sources will allow us to measure the multipolar structure of candidate black hole spacetimes. This will make it possible to test the no-hair theorem, and thereby to test the hypothesis that black hole candidates are in fact black holes are described by general relativity.

I will describe recent work by Cutler&Holz and Hirata, Holz, & Cutler showing that a highly sensitive, deci-Hz gravitational-wave mission like BBO or Decigo could measure cosmological parameters, such as the Hubble constant H_0 and the dark energy parameters w_0 and w_a, far more accurately than other proposed dark-energy missions. The basic point is that BBO’s angular resolution is so good that it will provide us with hundreds of thousands of “standard sirens.” These standard sirens are inspiraling neutron star and black hole binaries, with gravitationally-determined distances and optically determinable redshifts. I explain why a BBO-like mission would also be a powerful weak lensing mission, and I briefly describe some further astrophysics that would flow from such a mission.

It has long been recognized that there are two distinct laws that go by the name of the Second Law of Thermodynamics. The original says that there can be no process resulting in a net decrease in the total entropy of all bodies involved. A consequence of the kinetic theory of heat is that this law will not be strictly true; statistical fluctuations will result in small spontaneous transfers of heat from a cooler to a warmer body. The currently accepted version of the Second Law is probabilistic: tiny spontaneous transfers of heat from a cooler to a warmer body will be occurring all the time, while a larger transfer is not impossible, merely improbable. There can be no process whose expected result is a net decrease in total entropy. According to Maxwell, the Second Law has only statistical validity, and this statement is easily read as an endorsement of the probabilistic version. I argue that a close reading of Maxwell, with attention to his use of "statistical," shows that the version of the second law endorsed by Maxwell is strictly weaker than our probabilistic version. According to Maxwell, even the probable truth of the second law is limited to situations in which we deal with matter only in bulk and are unable to observe or manipulate individual molecules. Maxwell's version does not rule out a device that could, predictably and reliably, transfer heat from a cooler to a warmer body without a compensating increase in entropy. I will discuss the evidence we have for these two laws, Maxwell's and ours.

Constraints on the formation of primordial black holes - especially the ones which are small enough to evaporate - provide a unique probe of the early universe, high energy physics and extra dimensions. For evaporating black holes, the dominant constraints are associated with big bang nucleosynthesis and the extragalactic photon background, but there are also other limits associated with the cosmic microwave background, cosmic rays and various types of relic particles. For larger non-evaporating black holes, important constraints come from their gravitational and astrophysical effects. Small non-primordial evaporating black holes may be produced in the LHC if there are large extra dimensions and this would also have important implications for the early universe.

We study time dependent couplings in conformal field theories using rotating probe branes in AdS X S spacetimes. We find that induced metrics on the brane worldvolumes develop horizons with characteristic Hawking temperatures even when there is no black hole in the bulk. This framework is used to obtain toy models for quantum quench.

Combining the principles of general relativity and quantum theory still remains as elusive as ever. Recent work, that concentrated on one of the points of contact (and conflict) between quantum theory and general relativity, suggests a new perspective on gravity. It appears that the gravitational dynamics in a wide class of theories - including, but not limited to, standard Einstein's theory - can be given a purely thermodynamic interpretation. In this approach gravity appears as an emergent phenomenon, like e.g., gas or fluid dynamics. I will describe the necessary background, key results and their implications as suggested by my recent work in this area.

This talk will discuss some surprising links which have emerged in the last few years between two at first sight distinct areas of mathematical physics: the spectral properties of certain simple schroedinger-like equations, and the Bethe ansatz techniques which are used to compute the energies of states in integrable quantum field theories. No knowledge of either area will be assumed.

Quantization of string theory on the AdS(3) backgrounds with the RR flux, such as AdS(3)xS(3)xT(4) or AdS(3)xS(3)xS(3)xS(1), is an unsolved problem. Since the sigma model on these backgrounds is classically integrable, one can try to implement powerful methods of integrability similar to those used to solve AdS(5)/CFT(4) and AdS(4)/CFT(3). I will describe the integrability approach to the AdS(3) backgrounds, emphasizing the differences to the better understood cases of AdS(5) and AdS(4).