Physical Process Version of the First Law of Thermodynamics for Black Holes in Higher Dimensional Gravity

The problem of physical process version of the first law of black hole thermodynamics for charged rotating black hole in n-dimensional gravity is elaborated. The formulae for the first order variations of mass, angular momentum and canonical energy in Einstein (n-2)-gauge form field theory are derived. These variations are expressed by means of the perturbed matter energy momentum tensor and matter current density.Comment: 6 pages, REVTEX, to be published in Phys.Rev.D1

Physical process version of the first law of thermodynamics for black holes in Einstein-Maxwell axion-dilaton gravity

We derive general formulae for the first order variation of the ADM mass, angular momentum for linear perturbations of a stationary background in Einstein-Maxwell axion-dilaton gravity being the low-energy limit of the heterotic string theory. All these variations were expressed in terms of the perturbed matter energy momentum tensor and the perturbed charge current density. Combining these expressions we reached to the form of the {\it physical version} of the first law of black hole dynamics for the stationary black holes in the considered theory being the strong support for the cosmic censorship.Comment: 8 pages, Revte

Trapped surfaces in prolate collapse in the Gibbons-Penrose construction

We investigate existence and properties of trapped surfaces in two models of collapsing null dust shells within the Gibbons-Penrose construction. In the first model, the shell is initially a prolate spheroid, and the resulting singularity forms at the ends first (relative to a natural time slicing by flat hyperplanes), in analogy with behavior found in certain prolate collapse examples considered by Shapiro and Teukolsky. We give an explicit example in which trapped surfaces are present on the shell, but none exist prior to the last flat slice, thereby explicitly showing that the absence of trapped surfaces on a particular, natural slicing does not imply an absence of trapped surfaces in the spacetime. We then examine a model considered by Barrabes, Israel and Letelier (BIL) of a cylindrical shell of mass M and length L, with hemispherical endcaps of mass m. We obtain a "phase diagram" for the presence of trapped surfaces on the shell with respect to essential parameters $\lambda \equiv M/L$ and $\mu \equiv m/M$. It is found that no trapped surfaces are present on the shell when $\lambda$ or $\mu$ are sufficiently small. (We are able only to search for trapped surfaces lying on the shell itself.) In the limit $\lambda \to 0$, the existence or nonexistence of trapped surfaces lying within the shell is seen to be in remarkably good accord with the hoop conjecture.Comment: 22 pages, 6 figure

Conservation of the stress tensor in perturbative interacting quantum field theory in curved spacetimes

We propose additional conditions (beyond those considered in our previous papers) that should be imposed on Wick products and time-ordered products of a free quantum scalar field in curved spacetime. These conditions arise from a simple ``Principle of Perturbative Agreement'': For interaction Lagrangians $L_1$ that are such that the interacting field theory can be constructed exactly--as occurs when $L_1$ is a ``pure divergence'' or when $L_1$ is at most quadratic in the field and contains no more than two derivatives--then time-ordered products must be defined so that the perturbative solution for interacting fields obtained from the Bogoliubov formula agrees with the exact solution. The conditions derived from this principle include a version of the Leibniz rule (or ``action Ward identity'') and a condition on time-ordered products that contain a factor of the free field $\phi$ or the free stress-energy tensor $T_{ab}$. The main results of our paper are (1) a proof that in spacetime dimensions greater than 2, our new conditions can be consistently imposed in addition to our previously considered conditions and (2) a proof that, if they are imposed, then for {\em any} polynomial interaction Lagrangian $L_1$ (with no restriction on the number of derivatives appearing in $L_1$), the stress-energy tensor $\Theta_{ab}$ of the interacting theory will be conserved. Our work thereby establishes (in the context of perturbation theory) the conservation of stress-energy for an arbitrary interacting scalar field in curved spacetimes of dimension greater than 2. Our approach requires us to view time-ordered products as maps taking classical field expressions into the quantum field algebra rather than as maps taking Wick polynomials of the quantum field into the quantum field algebra.Comment: 88 pages, latex, no figures, v2: changes in the proof of proposition 3.

First Law of Black Rings Thermodynamics in Higher Dimensional Dilaton Gravity with p + 1 Strength Forms

We derive the first law of black rings thermodynamics in n-dimensional Einstein dilaton gravity with additional (p+1)-form field strength being the simplest generalization of five-dimensional theory containing a stationary black ring solution with dipole charge. It was done by means of choosing any cross section of the event horizon to the future of the bifurcation surface.Comment: 6 pages, to be published in Phys.Rev.D1

And what if gravity is intrinsically quantic ?

Since the early days of search for a quantum theory of gravity the attempts have been mostly concentrated on the quantization of an otherwise classical system. The two most contentious candidate theories of gravity, sting theory and quantum loop gravity are based on a quantum field theory - the latter is a quantum field theory of connections on a SU(2) group manifold and former a quantum field theory in two dimensional spaces. Here we argue that there is a very close relation between quantum mechanics and gravity. Without gravity quantum mechanics becomes ambiguous. We consider this observation as the evidence for an intrinsic relation between these fundamental laws of nature. We suggest a quantum role and definition for gravity in the context of a quantum universe, and present a preliminary formulation for gravity in a system with a finite number of particles.Comment: 8 pages, 1 figure. To appear in the proceedings of the DICE2008 conference, Castiglioncello, Tuscany, Italy, 22-26 Sep. 2008. V2: some typos remove

Wald's entropy is equal to a quarter of the horizon area in units of the effective gravitational coupling

The Bekenstein-Hawking entropy of black holes in Einstein's theory of gravity is equal to a quarter of the horizon area in units of Newton's constant. Wald has proposed that in general theories of gravity the entropy of stationary black holes with bifurcate Killing horizons is a Noether charge which is in general different from the Bekenstein-Hawking entropy. We show that the Noether charge entropy is equal to a quarter of the horizon area in units of the effective gravitational coupling on the horizon defined by the coefficient of the kinetic term of specific graviton polarizations on the horizon. We present several explicit examples of static spherically symmetric black holes.Comment: 20 pages ; added clarifications, explanations, new section on the choice of polarizations, results unchanged; replaced with published versio

Light-sheets and Bekenstein's bound

From the covariant bound on the entropy of partial light-sheets, we derive a version of Bekenstein's bound: S/M \leq pi x/hbar, where S, M, and x are the entropy, total mass, and width of any isolated, weakly gravitating system. Because x can be measured along any spatial direction, the bound becomes unexpectedly tight in thin systems. Our result completes the identification of older entropy bounds as special cases of the covariant bound. Thus, light-sheets exhibit a connection between information and geometry far more general, but in no respect weaker, than that initially revealed by black hole thermodynamics.Comment: 5 pages, 1 figure; v2: published version, improved discussion of weak gravity condition, final paragraph adde

Quantum field theory in curved spacetime, the operator product expansion, and dark energy

To make sense of quantum field theory in an arbitrary (globally hyperbolic) curved spacetime, the theory must be formulated in a local and covariant manner in terms of locally measureable field observables. Since a generic curved spacetime does not possess symmetries or a unique notion of a vacuum state, the theory also must be formulated in a manner that does not require symmetries or a preferred notion of a ``vacuum state'' and ``particles''. We propose such a formulation of quantum field theory, wherein the operator product expansion (OPE) of the quantum fields is elevated to a fundamental status, and the quantum field theory is viewed as being defined by its OPE. Since the OPE coefficients may be better behaved than any quantities having to do with states, we suggest that it may be possible to perturbatively construct the OPE coefficients--and, thus, the quantum field theory. By contrast, ground/vacuum states--in spacetimes, such as Minkowski spacetime, where they may be defined--cannot vary analytically with the parameters of the theory. We argue that this implies that composite fields may acquire nonvanishing vacuum state expectation values due to nonperturbative effects. We speculate that this could account for the existence of a nonvanishing vacuum expectation value of the stress-energy tensor of a quantum field occurring at a scale much smaller than the natural scales of the theory.Comment: 9 pages, essay awarded 4th prize by Gravity Research Foundatio

Hamiltonian of galileon field theory

We give a detailed calculation for the Hamiltonian of single galileon field theory, keeping track of all the surface terms. We calculate the energy of static, spherically symmetric configuration of the single galileon field at cubic order coupled to a point-source and show that the 2-branches of the solution possess energy of equal magnitude and opposite sign, the sign of which is determined by the coefficient of the kinetic term $\alpha_2$. Moreover the energy is regularized in the short distance (ultra-violet) regime by the dominant cubic term even though the source is divergent at the origin. We argue that the origin of the negativity is due to the ghost-like modes in the corresponding branch in the presence of the point source. This seems to be a non-linear manifestation of the ghost instability.Comment: 13 pages, 1 figur