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Alfred Molina

Publications and source records attributed to Alfred Molina.

15 recordsLinked to original sources
arXiv2018

An approximate global solution of Einstein's equations for a rotating two layers star

We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple two layers star model: a self-gravitating ball built up by two layers of perfect fluid having different linear equation of state moving in a rigid motion pattern. Using the post-Min\-kows\-kian formalism (weak-field approximation) and considering rotation as a perturbation (slow-rotation approximation), we find approximate interior and exterior (asymptotically flat) solutions to this problem in harmonic coordinates. Interior and exterior solutions are matched, in the sense described by Lichnerowicz, on the surfaces of constant pressure, to obtain a global solution.

gr-qc↗
arXiv2017

Generalized Gödel universes in higher dimensions and pure Lovelock gravity

Gödel universe is a homogeneous rotating dust with negative $Λ$ which is a direct product of three dimensional pure rotation metric with a line. We would generalize it to higher dimensions for Einstein and pure Lovelock gravity with only one $N$th order term. For higher dimensional generalization, we have to include more rotations in the metric, and hence we shall begin with the corresponding pure rotation odd $(d=2n+1)$-dimensional metric involving $n$ rotations, which eventually can be extended by a direct product with a line or a space of constant curvature for yielding higher dimensional Gödel universe. The considerations of $n$ rotations and also of constant curvature spaces is a new line of generalization and is being considered for the first time.

gr-qc↗
arXiv2016

Buchdahl-Vaidya-Tikekar model for stellar interior in pure Lovelock gravity - II

For a given Lovelock order $N$, it turns out that static fluid solutions of the pure Lovelock equation for a star interior have the universal behavior in all $n\geq 2N+2$ dimensions relative to an appropriately defined variable and the Vaidya-Tikekar parameter $K$, indicating deviation from sphericity of $3$-space geometry. We employ the Buchdahl metric ansatz which encompasses almost all the known physically acceptable models including in particular the Vaidya-Tikekar and Finch-Skea. Further for a given star radius, the constant density star, always described by the Schwarzschild interior solution, defines the most compact state of distribution while the other end is marked by the Finch-Skea model, and all the other physically tenable models lie in between these two limiting distributions.

gr-qc↗
arXiv2016

(Not so) pure Lovelock Kasner metrics

The gravitational interaction is expected to be modified for very short distances. This is particularly important in situations in which the curvature of spacetime is large in general, such as close to the initial cosmological singularity. The gravitational dynamics is then captured by the higher curvature terms in the action, making it difficult to reliably extrapolate any prediction of general relativity. In this note we review pure Lovelock equations for Kasner-type metrics. These equations correspond to a single $N$th order Lovelock term in the action in $d=2N+1,\,2N+2$ dimensions, and they capture the relevant gravitational dynamics when aproaching the big-bang singularity within the Lovelock family of theories. These are classified in several isotropy types. Some of these families correspond to degenerate classes of solutions, such that their dynamics is not completely determined by the equations of pure Lovelock gravity. Instead, these Kasner solutions become sensitive to the subleading terms in the Lovelock series.

gr-qc↗
arXiv2016

Higher dimensional generalization of Buchdahl-Vaidya-Tikekar model for super compact star

We obtain higher dimensional solutions for super compact star for the Buchdahl-Vaidya-Tikekar metric ansatz. In particular, Vaidya and Tikekar characterized the $3$-geometry by a parameter, $K$ which is related to the sign of density gradient. It turns out that the key pressure isotropy equation continues to have the same Gauss form, and hence $4$-dimensional solutions can be taken over to higher dimensions with $K$ satisfying the relation, $K_n = (K_4-n+4)/(n-3)$ where subscript refers to dimension of spacetime. Further $K\geq0$ is required else density would have undesirable feature of increasing with radius, and the equality indicates a constant density star described by the Schwarzschild interior solution. This means for a given $K_4$, maximum dimension could only be $n=K_4+4$, else $K_n$ will turn negative.

gr-qc↗
arXiv2015

Pure Lovelock Kasner metrics

We study pure Lovelock vacuum and perfect fluid equations for Kasner-type metrics. These equations correspond to a single $N$th order Lovelock term in the action in $d=2N+1,\,2N+2$ dimensions, and they capture the relevant gravitational dynamics when aproaching the big-bang singularity within the Lovelock family of theories. Pure Lovelock gravity also bears out the general feature that vacuum in the critical odd dimension, $d=2N+1$, is kinematic; i.e. we may define an analogue Lovelock-Riemann tensor that vanishes in vacuum for $d=2N+1$, yet the Riemann curvature is non-zero. We completely classify isotropic and vacuum Kasner metrics for this class of theories in several isotropy types. The different families can be characterized by means of certain higher order 4th rank tensors. We also analyze in detail the space of vacuum solutions for five and six dimensional pure Gauss-Bonnet theory. It possesses an interesting and illuminating geometric structure and symmetries that carry over to the general case. We also comment on a closely related family of exponential solutions and on the possibility of solutions with complex Kasner exponents. We show that the latter imply the existence of closed timelike curves in the geometry.

gr-qc↗
arXiv2015

On the meaning of Painlevé--Gullstrand synchronization

Following on from two recent papers, here we examine the relationship between Newtonian gravitation and general relativity in more depth. This allows us to define a scalar potential which is just the proper time of the vector potential when the latter is interpreted as the geodesic velocity field. The results are closely related to spacetimes that admit Painlevé--Gullstrand synchronization.

gr-qc↗
arXiv2013

Homothetic motions and Newtonian cosmology

We consider the homothetic motion group. We construct a homothetic covariant Newtonian gravitation theory which unifies inertial homothetic forces and gravitational fields. This is achieved through an equivalence principle based on a local homothetic frame of motion. As a consequence, we can obtain a coherent Newtonian cosmology which admits a cosmological principle and leads to the Friedman equations for a dust universe. Finally we prove that this gravity theory can be obtained as the non-relativistic limit of a class of metrics in General Relativity. The Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) metric and its limit are also studied.

gr-qc↗
arXiv2013

Wahlquist's metric versus an approximate solution with the same equation of state

We compare an approximation of the singularity-free Wahlquist exact solution with a stationary and axisymmetric metric for a rigidly rotating perfect fluid with the equation of state $μ+ 3p= μ_0$, a sub-case of a global approximate metric obtained recently by some of us. We see that to have a fluid with vanishing twist vector everywhere in Wahlquist's metric the only option is to let its parameter $r_0\rightarrow0$ and using this in the comparison allows us in particular to determine the approximate relation between the angular velocity of the fluid in a set of harmonic coordinates and $r_0$. Through some coordinate changes we manage to make every component of both approximate metrics equal. In this situation, the free constants of our metric take values that happen to be those needed for it to be of Petrov type D, the last condition that this fluid must verify to give rise to the Wahlquist solution.

gr-qc↗
arXiv2013

An approximate global solution of Einstein's equation for a rotating compact source with linear equation of state

We use analytic perturbation theory to present a new approximate metric for a rigidly rotating perfect fluid source with equation of state (EOS) $ε+(1-n)p=ε_0$. This EOS includes the interesting cases of strange matter, constant density and the fluid of the Wahlquist metric. It is fully matched to its approximate asymptotically flat exterior using Lichnerowicz junction conditions and it is shown to be a totally general matching using Darmois-Israel conditions and properties of the harmonic coordinates. Then we analyse the Petrov type of the interior metric and show first that, in accordance with previous results, in the case corresponding to Wahlquist's metric it can not be matched to the asymptotically flat exterior. Next, that this kind of interior can only be of Petrov types I, D or (in the static case) O and also that the non-static constant density case can only be of type I. Finally, we check that it can not be a source of Kerr's metric.

gr-qc↗
arXiv2013

Comparing results for a global metric from analytical perturbation theory and a numerical code

We compare the results obtained from analytical perturbation theory and the AKM numerical code for an axistationary spacetime built from matching a rotating perfect fluid interior with the equation of state $ε-3p=4B$ of the simple MIT bag model and an asymptotically flat exterior. We discuss the behaviour of the error in the metric components of the analytical approximation going to higher orders. Additionally, we check and comment the errors in multipole moments, central pressure and some other physical properties of the spacetime.

gr-qc↗
arXiv2012

Rigid motions and generalized Newtonian gravitation. Lost in Translation

We try to lay down the foundations of a Newtonian theory where inertia and gravitational fields appear in a unified way aiming to reach a better understanding of the general relativistic theory. We also formulate a kind of equivalence principle for this generalized Newtonian theory. Finally we find the non-relativistic limit of the Einstein's equations for the space--time metric derived from the Newtonian theory.

gr-qc↗
arXiv2012

Comparison of metrics obtained with analytic perturbation theory and a numerical code

We compare metrics obtained through analytic perturbation theory with their numerical counterparts. The analytic solutions are computed with the CMMR post-Minkowskian and slow rotation approximation due to Cabezas et al. (2007) for an asymptotically flat stationary spacetime containing a rotating perfect fluid compact source. The same spacetime is studied with the AKM numerical multi-domain spectral code (Ansorg et al., 2002,2003). We then study their differences inside the source, near the infinity and in the matching surface, or equivalently, the global character of the analytic perturbation scheme.

gr-qc↗
arXiv2008

On Kaluza-Klein spacetime in Einstein-Gauss-Bonnet gravity

By considering the product of the usual four dimensional spacetime with two dimensional space of constant curvature, an interesting black hole solution has recently been found for Einstein-Gauss-Bonnet gravity. It turns out that this as well as all others could easily be made to radiate Vaidya null dust. However there exists no Kerr analogue in this setting. To get the physical feel of the four dimensional black hole spacetimes, we study asymptotic behavior of stresses at the two ends, $r\to0$ and $r\to\infty$.

gr-qc↗