Discos de acreción y teorías métricas de gravitación

La luminosidad de un disco de acreción alrededor de un objeto compacto está dad por: L=(1-E(rₒ))c²dM/dt, donde dM/dt es la masa por unidad de tiempo que entra al disco y E(rₒ) es la energía en la última órbita circular estable vista desde el infinito dividido, la energía en reposo. Se calcula esta energía y la frecuencia máxima vista desde el infinito vₘ usando la métrica estática con simetría esférica más general. Luego se usan las fórmulas obtenidas para hacer cálculos con métricas particulares, distintas de la de Schwarschild, para ver como varían R(rₒ) y vₘ con la teoría de gravitación utilizada.Asociación Argentina de Astronomí

The neutron stars structure in metric theories of gravitation

From the variational principle for the total internal energy of a neutrons star and some restrictions on the form of the metric coefficients, we have found equations of equilibrium which are valid for every metric theory of gravitation. We also present some simple solutions of the equations to find the neutron stars maximum mass.Asociación Argentina de Astronomí

Ultrarelativistic black hole in an external electromagnetic field and gravitational waves in the Melvin universe

We investigate the ultrarelativistic boost of a Schwarzschild black hole immersed in an external electromagnetic field, described by an exact solution of the Einstein-Maxwell equations found by Ernst (the ``Schwarzschild-Melvin'' metric). Following the classical method of Aichelburg and Sexl, the gravitational field generated by a black hole moving ``with the speed of light'' and the transformed electromagnetic field are determined. The corresponding exact solution describes an impulsive gravitational wave propagating in the static, cylindrically symmetric, electrovac universe of Melvin, and for a vanishing electromagnetic field it reduces to the well known Aichelburg-Sexl pp-wave. In the boosting process, the original Petrov type I of the Schwarzschild-Melvin solution simplifies to the type II on the impulse, and to the type D elsewhere. The geometry of the wave front is studied, in particular its non-constant Gauss curvature. In addition, a more general class of impulsive waves in the Melvin universe is constructed by means of a six-dimensional embedding formalism adapted to the background. A coordinate system is also presented in which all the impulsive metrics take a continuous form. Finally, it is shown that these solutions are a limiting case of a family of exact gravitational waves with an arbitrary profile. This family is identified with a solution previously found by Garfinkle and Melvin. We thus complement their analysis, in particular demonstrating that such spacetimes are of type II and belong to the Kundt class.Comment: 11 pages, REVTeX

Impulsive waves in the Nariai universe

A new class of exact solutions is presented which describes impulsive waves propagating in the Nariai universe. It is constructed using a six-dimensional embedding formalism adapted to the background. Due to the topology of the latter, the wave front consists of two non-expanding spheres. Special sub-classes representing pure gravitational waves (generated by null particles with an arbitrary multipole structure) or shells of null dust are analyzed in detail. Smooth isometries of the metrics are briefly discussed. Furthermore, it is shown that the considered solutions are impulsive members of a more general family of radiative Kundt spacetimes of type-II. A straightforward generalization to impulsive waves in the anti-Nariai and Bertotti-Robinson backgrounds is described. For a vanishing cosmological constant and electromagnetic field, results for well known impulsive pp-waves are recovered.Comment: 9 pages, 4 figures, REVTeX 4. v3: added Appendix B, revised references, minor changes in the text. To appear in Phys. Rev.

Mass Spectrum of Strings in Anti de Sitter Spacetime

We perform string quantization in anti de Sitter (AdS) spacetime. The string motion is stable, oscillatory in time with real frequencies $\omega_n= \sqrt{n^2+m^2\alpha'^2H^2}$ and the string size and energy are bounded. The string fluctuations around the center of mass are well behaved. We find the mass formula which is also well behaved in all regimes. There is an {\it infinite} number of states with arbitrarily high mass in AdS (in de Sitter (dS) there is a {\it finite} number of states only). The critical dimension at which the graviton appears is $D=25,$ as in de Sitter space. A cosmological constant $\Lambda\neq 0$ (whatever its sign) introduces a {\it fine structure} effect (splitting of levels) in the mass spectrum at all states beyond the graviton. The high mass spectrum changes drastically with respect to flat Minkowski spacetime. For $\Lambda\sim \mid\Lambda\mid N^2,$ {\it independent} of $\alpha',$ and the level spacing {\it grows} with the eigenvalue of the number operator, $N.$ The density of states $\rho(m)$ grows like \mbox{Exp}[(m/\sqrt{\mid\Lambda\mid}\;)^{1/2}] (instead of \rho(m)\sim\mbox{Exp}[m\sqrt{\alpha'}] as in Minkowski space), thus {\it discarding} the existence of a critical string temperature. For the sake of completeness, we also study the quantum strings in the black string background, where strings behave, in many respects, as in the ordinary black hole backgrounds. The mass spectrum is equal to the mass spectrum in flat Minkowski space.Comment: 31 pages, Latex, DEMIRM-Paris-9404

Perturbative solution to the back reaction problem in static space times

Se proyectan las ecuaciones de Einstein sobre una 3-superficie tipo espacial, considerando explícitamente que tomamos un espacio-tiempo estático. Luego, dentro de esta 3-superficie, hacemos una nueva proyección para expresar las ecuaciones de Einstein en términos de la curvatura bidimensional. El sistema de ecuaciones así planteado es equivalente a las ecuaciones de Einstein en 4 dimensiones. Buscando una solución a las mismas, se supone que el problema tiene simetría esférica. En este caso se logran desacoplar las ecuaciones y se halla una ecuación integral que puede ser iterada para hallar la solución perturbativa al problema. Como primer ejemplo de aplicación de este método, estudiaremos el efecto de back reaction producido por la creación cuántica de partículas sobre la métrica Scwarzschild. Así se utilizan los de la literatura, hallados recientemente, para resolver las ecuaciones semi-clásicas de Einstein, i.e. R_μ^ν - 1/2R δ_μ^ν= . Se hallaron expresiones analíticas para los coeficientes de la métrica corregida a un "loop" para el en el vacío de Hartle_Hawking-Israel, para un campo escalar no masivo. Utilizando estos resultados se puede estimar la corrección a la emisión de Hawking en el régimen cuasi-estático. Hallándose para la temperatura de emisión: T=(8πM)⁻¹ |1+(Mₚ/M)²/36π|, donde Mₚ=(KG/c³)^(1/2). Con esta temperatura y la corrección al área del horizonte, se hallan los nuevos valores de la cantidad de energía emitida y del tiempo de vida del agujero negro.Asociación Argentina de Astronomí