Einstein's Field Equations for the Interior of a Uniformly Rotating Stationary Axisymmetric Perfect Fluid

We reduce Einstein's field equations for the interior of a uniformly rotating, axisymmetric perfect fluid to a system of six second order partial differential equations for the pressure p the energy density $\mu$ and four dependent variables.Four of these equations do not depend on p and $\mu$ and the other two determine p and $\mu$

Black Hole in a Model with Dilaton and Monopole Fields

We present an exact black hole solution in a model having besides gravity a dilaton and a monopole field. The solution has three free parameters, one of which can be identified with the monopole charge, and another with the ADM mass. The metric is asymptotically flat and has two horizons and irremovable singularity only at $r=0$. The dilaton field is singular only at $r=0$. The dominant and the strong energy condition are satisfied outside and on the external horizon. According to a formulation of the no hair conjecture the solution is "hairy". Also the well know GHS-GM solution is obtained from our solution for certain values of its parameters.Comment: Selected for Honorable Mention in the Gravity Research Foundation Essay Competition, 2006, 7 page

Family Of Rotating Anisotropic Fluid Solutions which Match to Kerr's Solution

We present a family of exact rotating anisotropic fluid solutions, which satisfy all energy conditions for certain values of their parameters. The components of the Ricci tensor $R_{\mu\nu}$ the eigenvalues of the tensor $R_\mu^\nu$ and the energy-momentum tensor $T_{\mu\nu}$ of the solutions are given explicitly. All members of the family have the ring singularity of Kerr's solution and most of them one or two more singularities. The solutions can be matched to the solution of Kerr on three closed surfaces, which for proper values of the parameters of the solutions approximate oblate spheroids. All matching surfaces are thin shells. For some values of a constant the surface density in one of them is positive everywhere and in this surface and in its interior all energy conditions are satisfied.Comment: Published version in IJMP

Rotating Black Hole Solutions with Axion Dilaton and Two Vector Fields and Solutions with Metric and Fields of the Same Form

We present two rotating black hole solutions with axion $\xi$, dilaton $\phi$ and two U(1) vector fields. By applying the "Newman-Janis trick" to a metric with 3 arbitrary parameters we find a rotating metric $g_{\mu\nu}$ with 4 such parameters $(M, a, Q_E, Q_M)$, and then a solution with this $g_{\mu\nu}$ as metric. Our solution is asymptotically flat and has angular momentum $J=M a$, gyromagnetic ratio $g=2$, two horizons, the singularities of Kerr's solution, axion and dilaton singular only for $r=a\cos\theta=0$. Applying to the solution we have found the $S-$duality transformation we get a new solution, whose axion, dilaton and vector fields have one more parameter. The metric, each vector field and the $\lambda=\xi+ie^{-2\phi}$ of our solutions and the solution of : Sen for $Q_E$, Sen for $Q_E$ and $Q_M$, Kerr-Newman for $Q_E$ and $Q_M$, Kerr, Ref. 9, STW, GM-GHS, Reissner-Nordstr\"{o}m,Schwarzschild are the same function of $a$, and two functions $\rho^2=r(r+b)+a^2\cos^2\theta$ and $\Delta=\rho^2-2Mr+c$, of $a$, $b$ and two functions, and of $a$, $b$ and $d$ respectively, where $a$, $b$, $c$ and $d$ are constants. It is shown that from our solutions a number of known solutions can be obtained, which together with our solutions are listed in an Appendix. Also it is shown that all solutions which are mentioned in the paper satisfy all energy conditions, and mass formulae are obtained for them.Comment: 50 page

Finite element inversion of DInSAR data from the Mw 6.3 L’Aquila earthquake, 2009 (Italy)

Fault slip distribution is usually retrieved from geodetic data assuming that the local crust is an elastic, homogeneous and isotropic half‐space. In the last decades spatially dense geodetic data (e.g., DInSAR maps) have highlighted complex patterns of coseismic deformation that require new modeling tools, such as numerical methods, able to represent rheological and geometrical complexities of the Earth’s crust. In this work, we develop a procedure to perform inversion of geodetic data based on the finite element method, accounting for a more realistic description of the local crust. The method is applied to the 2009 L’Aquila earthquake (Mw 6.3), using DInSAR images of the coseismic displacement. Results highlight the non‐negligible influence of the medium structure: homogeneous and heterogeneous models show discrepancies up to 20% in the fault slip distribution values. Furthermore, in the heterogeneous models a new area of slip appears above the hypocenter. We also perform a resolution study, showing that the information about fault slip distributions retrieved from geodetic data should be considered as averaged on surrounding patches

Contact symmetry of time-dependent Schr\"odinger equation for a two-particle system: symmetry classification of two-body central potentials

Symmetry classification of two-body central potentials in a two-particle Schr\"{o}dinger equation in terms of contact transformations of the equation has been investigated. Explicit calculation has shown that they are of the same four different classes as for the point transformations. Thus in this problem contact transformations are not essentially different from point transformations. We have also obtained the detailed algebraic structures of the corresponding Lie algebras and the functional bases of invariants for the transformation groups in all the four classes

Dilatonic interpolation between Reissner-Nordstrom and Bertotti-Robinson spacetimes with physical consequences

We give a general class of static, spherically symmetric, non-asymptotically flat and asymptotically non-(anti) de Sitter black hole solutions in Einstein-Maxwell-Dilaton (EMD) theory of gravity in 4-dimensions. In this general study we couple a magnetic Maxwell field with a general dilaton potential, while double Liouville-type potentials are coupled with the gravity. We show that the dilatonic parameters play the key role in switching between the Bertotti-Robinson and Reissner-Nordstr\"om spacetimes. We study the stability of such black holes under a linear radial perturbation, and in this sense we find exceptional cases that the EMD black holes are unstable. In continuation we give a detailed study of the spin-weighted harmonics in dilatonic Hawking radiation spectrum and compare our results with the previously known ones. Finally, we investigate the status of resulting naked singularities of our general solution when probed with quantum test particles.Comment: 27 pages, 4 figures, to appear in CQG

PARP inhibitors in metastatic prostate cancer

Poly-ADP ribose polymerase inhibitors (PARPi) are an emerging therapeutic option for the treatment of prostate cancer. Their primary mechanism of action is via induction of synthetic lethality in cells with underlying deficiencies in homologous recombination repair (HRR). In men with metastatic castrate-resistant prostate cancer (mCRPC) and select HRR pathway alterations, PARPi treatment has been shown to induce objective tumor responses as well as improve progression free and overall survival. Presently, there are two PARPi, olaparib and rucaparib, that are FDA approved in the treatment of mCRPC. Ongoing research is focused on identifying which HRR alterations are best suited to predict response to PARPi so that these therapies can be most effectively utilized in the clinic. While resistance to PARPi remains a concern, combination therapies may represent a mechanism to overcome or delay resistance