A new final state of gravitational collapse is proposed. By extending the concept of Bose–Einstein condensation to gravitational systems, a cold, dark, compact object with an interior de Sitter condensate p _v = -ρ _v and an exterior Schwarzschild geometry of arbitrary total mass M is constructed. These regions are separated by a shell with a small but finite proper thickness ℓ of fluid with equation of state p = +ρ , replacing both the Schwarzschild and de Sitter classical horizons. The new solution has no singularities, no event horizons, and a global time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, which is of the order k _B ℓ Mc / , instead of the Bekenstein–Hawking entropy formula, S _BH = 4 π k _B GM ² / c . Hence, unlike black holes, the new solution is thermodynamically stable and has no information paradox.

A new final endpoint of complete gravitational collapse is proposed. By extending the concept of Bose–Einstein condensation to gravitational systems, a static, spherically symmetric solution to Einstein’s equations is obtained, characterized by an interior de Sitter region of $p=-\rho$ gravitational vacuum condensate and an exterior Schwarzschild geometry of arbitrary total mass M. These are separated by a phase boundary with a small but finite thickness ℓ, replacing both the Schwarzschild and de Sitter classical horizons. The resulting collapsed cold, compact object has no singularities, no event horizons, and a globally defined Killing time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, which is of order $k_B\ell Mc/\hslash$, instead of the Bekenstein–Hawking entropy, $S_{BH}=4\pi k_{B}G{M}^2/\hslash c$. Unlike BHs, a collapsed star of this kind is consistent with quantum theory, thermodynamically stable, and suffers from no information paradox.

We present a general method of deriving the effective action for conformal anomalies in any even dimension, which satisfies the Wess-Zumino consistency condition by construction. The method relies on defining the coboundary operator of the local Weyl group, $g_{\mathrm{ab}}\to \exp (2\mathrm{}\sigma {)g}_{\mathrm{ab}},$ and giving a cohomological interpretation to counterterms in the effective action in dimensional regularization with respect to this group. Nontrivial cocycles of the Weyl group arise from local functionals that are Weyl invariant in and only in the physical even integer dimension $d=2k.\mathrm{}$ In the physical dimension the nontrivial cocycles generate covariant nonlocal action functionals characterized by sensitivity to global Weyl rescalings. The nonlocal action so obtained is unique up to the addition of trivial cocycles and Weyl invariant terms, both of which are insensitive to global Weyl rescalings. These distinct behaviors under rigid dilations can be used to distinguish between infrared relevant and irrelevant operators in a generally covariant manner. Variation of the $d=4\mathrm{}$ nonlocal effective action yields two new conserved geometric stress tensors with local traces equal to the square of the Weyl tensor and the Gauss-Bonnet-Euler density, respectively. The second of these conserved tensors becomes ${}^{\mathrm{}\left(3\right)\mathrm{}}{H}_{\mathrm{ab}}$ in conformally flat spaces, exposing the previously unsuspected origin of this tensor. The method may be extended to any even dimension by making use of the general construction of conformal invariants given by Fefferman and Graham. As a corollary, conformal field theory (CFT) behavior of correlators at the asymptotic infinity of either anti–de Sitter or de Sitter spacetimes follows, i.e., ${\mathrm{AdS}}_{d+1\mathrm{}}-$ or ${\mathrm{deS}}_{d+1\mathrm{}}-{\mathrm{CFT}}_d$ correspondence. The same construction naturally selects all infrared relevant terms (and only those terms) in the low energy effective action of gravity in any even integer dimension. The infrared relevant terms arising from the known anomalies in $d=4\mathrm{}$ imply that the classical Einstein theory is modified at large distances.

We show that global de Sitter space is unstable to particle creation, even for a massive free field theory with no self-interactions. The $O(4,1)$ de Sitter invariant state is a definite phase coherent superposition of particle and antiparticle solutions in both the asymptotic past and future and, therefore, is not a true vacuum state. In the closely related case of particle creation by a constant, uniform electric field, a time symmetric state analogous to the de Sitter invariant one is constructed, which is also not a stable vacuum state. We provide the general framework necessary to describe the particle creation process, the mean particle number, and dynamical quantities such as the energy-momentum tensor and current of the created particles in the de Sitter and electric field backgrounds respectively in real time, establishing the connection to kinetic theory. We compute the energy-momentum tensor for adiabatic vacuum states in de Sitter space initialized at early times in global ${\mathbb{S}}^3$ sections and show that particle creation in the contracting phase results in exponentially large energy densities at later times, necessitating an inclusion of their backreaction effects and leading to large deviation of the spacetime from global de Sitter space before the expanding phase can begin.