Bose-Einstein condensed supermassive black holes: a case of renormalized quantum field theory in curved space-time

This paper investigates the question whether a realistic black hole can be in principal similar to a star, having a large but finite redshift at its horizon. If matter spreads throughout the interior of a supermassive black hole with mass $M\sim10^9M_\odot$, it has an average density comparable to air and it may arise from a Bose-Einstein condensate of densely packed H-atoms. Within the Relativistic Theory of Gravitation with a positive cosmological constant, a bosonic quantum field describing H atoms is coupled to the curvature scalar with dimensionless coupling $\xi$. In the Bose-Einstein condensed groundstate an exact, self-consistent solution for the metric occurs for a certain large value of $\xi$, quadratic in the black hole mass. It is put forward that $\xi$ is set by proper choice of the background metric as a first step of a renormalization approach, while otherwise the non-linearities are small. The black hole has a hair, the binding energy. Fluctuations about the ground state are considered.Comment: 18 pages Latex Physica E styl

The Marriage Problem and the Fate of Bachelors

In the marriage problem, a variant of the bi-parted matching problem, each member has a `wish-list' expressing his/her preference for all possible partners; this list consists of random, positive real numbers drawn from a certain distribution. One searches the lowest cost for the society, at the risk of breaking up pairs in the course of time. Minimization of a global cost function (Hamiltonian) is performed with statistical mechanics techniques at a finite fictitious temperature. The problem is generalized to include bachelors, needed in particular when the groups have different size, and polygamy. Exact solutions are found for the optimal solution (T=0). The entropy is found to vanish quadratically in $T$. Also other evidence is found that the replica symmetric solution is exact, implying at most a polynomial degeneracy of the optimal solution. Whether bachelors occur or not, depends not only on their intrinsic qualities, or lack thereof, but also on global aspects of the chance for pair formation in society.Comment: 14 pages revtex, submitted to Physica

How Zwicky already ruled out modified gravity theories without dark matter

Various theories, such as MOND, MOG, Emergent Gravity and $f(R)$ theories avoid dark matter by assuming a change in General Relativity and/or in Newton's law. Galactic rotation curves are typically described well. Here the application to galaxy clusters is considered, focussed on the good lensing and X-ray data for A1689. As a start, the no-dark-matter case is confirmed to work badly: the need for dark matter starts near the cluster centre, where Newton's law is still supposed to be valid. This leads to the conundrum discovered by Zwicky, which is likely only solvable in his way, namely by assuming additional (dark) matter. Neutrinos with eV masses serve well without altering the successes in (dwarf) galaxies.Comment: 10 pages, 2 figures. Matches published versio

Thermodynamic picture of the glassy state gained from exactly solvable models

A picture for thermodynamics of the glassy state was introduced recently by us (Phys. Rev. Lett. {\bf 79} (1997) 1317; {\bf 80} (1998) 5580). It starts by assuming that one extra parameter, the effective temperature, is needed to describe the glassy state. This approach connects responses of macroscopic observables to a field change with their temporal fluctuations, and with the fluctuation-dissipation relation, in a generalized, non-equilibrium way. Similar universal relations do not hold between energy fluctuations and the specific heat. In the present paper the underlying arguments are discussed in greater length. The main part of the paper involves details of the exact dynamical solution of two simple models introduced recently: uncoupled harmonic oscillators subject to parallel Monte Carlo dynamics, and independent spherical spins in a random field with such dynamics. At low temperature the relaxation time of both models diverges as an Arrhenius law, which causes glassy behavior in typical situations. In the glassy regime we are able to verify the above mentioned relations for the thermodynamics of the glassy state. In the course of the analysis it is argued that stretched exponential behavior is not a fundamental property of the glassy state, though it may be useful for fitting in a limited parameter regime.Comment: revised version, 38 pages, 9 figure

Exact Schwarzschild-de Sitter black holes in a family of massive gravity models

The Schwarzschild-de Sitter and Reissner-Nordstr\"om-de Sitter black hole metrics appear as exact solutions in the recently formulated massive gravity of de Rham, Gabadadze and Tolley (dRGT), where the mass term sets the curvature scale. They occur within a two-parameter family of dGRT mass terms. They show no trace of a cloud of scalar graviton modes, and in the limit of vanishing graviton mass they go smoothly to the Schwarzschild and Reissner-Nordstr\"om metrics.Comment: 4 page