15382595
Hamiltonian thermodynamics of a Lovelock black hole
We consider the Hamiltonian dynamics and thermodynamics of spherically symmetric spacetimes within a one-parameter family of five-dimensional Lovelock theories. We adopt boundary conditions that make every classical solution part of a black hole exterior, with the spacelike hypersurfaces extending from the horizon bifurcation three-sphere to a timelike boundary with fixed intrinsic metric. The constraints are simplified by a Kuchar ˇ-type canonical transformation, and the theory is reduced to its true dynamical degrees of freedom. After quantization, the trace of the analytically continued Lorentzian time evolution operator is interpreted as the partition function of a thermodynamical canonical ensemble. Whenever the partition function is dominated by a Euclidean black hole solution, the entropy is given by the Lovelock analogue of the Bekenstein-Hawking entropy; in particular, in the low temperature limit the system exhibits a dominant classical solution that has no counterpart in Einstein’s theory. The asymptotically flat space limit of the partition function does not exist. The results indicate qualitative robustness of the thermodynamics of five-dimensional Einstein theory upon the addition of a nontrivial Lovelock term. @S0556-2821~97!03806-X#
7991045
Unitarity of interacting fields in curved spacetime.
On globally hyperbolic spacetimes, each foliation by spacelike hypersurfaces corresponds to a Hamiltonian description of field theory, and unitarity follows formally from the Hermiticity of the Hamiltonian. For a renormalizable theory, unitarity at each order in perturbation theory follows from the corresponding Hermiticity of each term in the time-ordered product of interaction Hamiltonians. For more general spacetimes, one can still use the path integral to obtain a generalized Lehmann-Symanzik-Zimmermann reduction formula for $S$-matrix elements and the corresponding perturbative expansion. Unitarity imposes an infinite set of identities on the scattering amplitudes, which are the generalizations of the flat-spacetime Cutkosky rules. We find these explicitly to $O({\ensuremath{\lambda}}^{3})$ in a $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}$ theory, and show how to find the relations to any order. For globally hyperbolic spacetimes the unitarity identities are satisfied [at least to $O({\ensuremath{\lambda}}^{3})$] because of a single property of the configuration-space propagator that reflects the causal structure of the spacetime.
7802314
Einstein equation with quantum corrections reduced to second order.
We consider the Einstein equation with first-order (semiclassical) quantum corrections. Although the quantum corrections contain up to fourth-order derivatives of the metric, the solutions which are physically relevant satisfy reduced equations which contain derivatives no higher than second order. We obtain the reduced equations for a range of stress-energy tensors. These reduced equations are suitable for a numerical solution, are expected to contain fewer numerical instabilities than the original fourth-order equations, and yield only physically relevant solutions. We give analytic and numerical solutions or reduced equations for particular examples, including Friedmann-Lema\^{\i}tre universes with a cosmological constant, a spherical body of constant density, and more general conformally flat metrics.
116957296
Higher derivative expansions and non-locality, with applications to gravity and the stability of flat space
15289059
Black hole evaporation and higher-derivative gravity
We examine the role which higher-derivative gravity interactions may play in black hole evaporation. The thermodynamic properties of black holes in Lovelock gravity are described. In certain cases, the specific heat of a black hole becomes positive at a small mass. This results in an infinite lifetime for the black hole (and also allows it to achieve stable equilibrium with a thermal environment). Thus no conflict with unitary time evolution would arise in such theories.
15433766
Black-hole thermodynamics in Lovelock gravity.
The thermodynamic properties of black holes in Lovelock gravity are examined. In particular, the case of the Einstein Lagrangian plus the four-dimensional Euler density is discussed in detail. In five dimensions, one finds that the specific heat of a black hole becomes positive at small mass, allowing the black hole to achieve stable equilibrium with its environment and giving it an infinite lifetime. This behavior is not universal, however, but it always occurs in 2k+1 dimensions for a Lovelock theory including the 2k-dimensional Euler density. For theories including six-derivative or higher-order interactions, black holes with degenerate zero-temperature horizons are also possible.
5102322
Quantum entanglement of localized excited states at finite temperature
A bstractIn this work we study the time evolutions of (Renyi) entanglement entropy of locally excited states in two dimensional conformal field theories (CFTs) at finite temperature. We consider excited states created by acting with local operators on thermal states and give both field theoretic and holographic calculations. In free field CFTs, we find that the growth of Renyi entanglement entropy at finite temperature is reduced compared to the zero temperature result by a small quantity proportional to the width of the localized excitations. On the other hand, in finite temperature CFTs with classical gravity duals, we find that the entanglement entropy approaches a characteristic value at late time. This behaviour does not occur at zero temperature. We also study the mutual information between the two CFTs in the thermofield double (TFD) formulation and give physical interpretations of our results.
882035
Black holes in supergravity: the non-BPS branch
We construct extremal, spherically symmetric black hole solutions to 4D supergravity with charge assignments that preclude BPS-saturation. In particular, we determine the ground state energy as a function of charges and moduli. We find that the mass of the non-BPS black hole remains that of a marginal bound state of four basic constituents throughout the entire moduli space and that there is always a non-zero gap above the BPS bound.
55066831
The electrostatic view on M-theory LLM geometries
We describe the geometry of the $ \mathbb{R} \times {\text{SO}}(3) \times {\text{SO}}(6) \times {\text{U}}(1) $ invariant half-BPS M-theory configurations considered in LLM in terms of their electrostatic variables. We discuss both regular configurations, such as AdS4 × S7 and AdS7 × S4 vacua or simple excited solutions, and singular ones such as the superstar geometries. This allows us to identify the appropriate boundary conditions describing the most general smooth and superstar-like singular configurations. We also compute their masses, matching the expected result from their microscopic interpretation, but now at finite radius of curvature.
119567009
Yang-Mills equations are formally linearizable
It is proved, in the framework of a recent theory of non-linear group representations elaborated by the authors, that the non-linear Yang-Mills equations are formally linearizable: there exists a formal non-linear operator which intertwins the non-linear Yang-Mills equations with their free (linear) part.
140116815
What is a chiral 2 d CFT ? And what does it have to do with extremal black holes ?
The near horizon limit of the extremal BTZ black hole is a “self-dual orbifold” of AdS3. This geometry has a null circle on its boundary, and thus the dual field theory is a Discrete Light Cone Quantized (DLCQ) two dimensional CFT. The same geometry can be compactified to two dimensions giving AdS2 with a constant electric field. The kinematics of the DLCQ show that in a consistent quantum theory of gravity in these backgrounds there can be no dynamics in AdS2, which is consistent with older ideas about instabilities in this space. We show how the necessary boundary conditions eliminating AdS2 fluctuations can be implemented, leaving one copy of a Virasoro algebra as the asymptotic symmetry group. Our considerations clarify some aspects of the chiral CFTs appearing in proposed dual descriptions of the near-horizon degrees of freedom of extremal black holes.