Modern Physics Letters A

The source theory provides a straightforward way to obtain the Newton’s potential upon establishing the vacuum-to-vacuum transition amplitude in quantized Einstein theory of gravity. Here, we use the same method to derive the gravitational potential of two static point masses in f(R) = R + aR² gravity.

The $\gamma$-bands are analyzed through the variation of the energy of the $2_{\gamma }^{+}$ excitation and the energies of excited level sequence of $\gamma$-bands with respect to various parameters. The shape phase transition observed at N = 88–90 is reviewed through its influence on the energies of $\gamma$-band. The correlation of the $2_{\gamma }^{+}$ excitation energies with the collective shape signature observable $R_{4/2}$ indicates a connection with the nuclear equilibrium structure. The study of excited level sequence in the $\gamma$-band with respect to the ground band signifies that the two bands differ in deformation.

Our purpose in this paper is to modify the original proximity potential by universal function available in the literature. A potential model with Yukawa proximity potential has been considered according to the modified model fusion reactions of ${}^{92}\mathrm{\text{Zr}}+{}^{12}\mathrm{\text{C}}$, ${}^{16}\mathrm{\text{O}}+{}^{92}\mathrm{\text{Zr}}$, ${}^{28}\mathrm{\text{Si}}+{}^{92}\mathrm{\text{Zr}}$, ${}^{16}\mathrm{\text{O}}+{}^{144}\mathrm{\text{m}}$, ${}^{28}\mathrm{\text{Si}}+{}^{28}\mathrm{\text{Si}}$, ${}^{28}\mathrm{\text{Si}}+{}^{29}\mathrm{\text{Si}}$, ${}^{28}\mathrm{\text{Si}}+{}^{30}\mathrm{\text{Si}}$, ${}^{24}\mathrm{\text{Mg}}+{}^{24}\mathrm{\text{Mg}}$, ${}^{24}\mathrm{\text{Mg}}+{}^{26}\mathrm{\text{Mg}}$ and ${}^{24}\mathrm{\text{Mg}}+{}^{28}\mathrm{\text{Si}}$, ${}^{26}\mathrm{\text{Mg}}+{}^{28}\mathrm{\text{Si}}$, ${}^{24}\mathrm{\text{Mg}}+{}^{30}\mathrm{\text{Si}}$, ${}^{26}\mathrm{\text{Mg}}+{}^{30}\mathrm{\text{Si}}$ which have been discussed in detail. The results have a good agreement with the experimental data.

In this paper, we construct a new time-periodic solution and a new time-machine solution according to the general form of the new family of solutions to the Einstein’s vacuum field equations with cosmological constant. The time-periodic solutions have some relations with the loop universe. The time-machine solutions are spacetime configurations including closed time-like curves (CTCs), and allowing physical observers to return to their own past. This problem has been of concern a lot recently. We expect the new solutions obtained in this paper can be applied in modern cosmology and general relativity.

This paper discusses the approximate Noether symmetries of the action of plane symmetric spacetime. A time-dependent conformal factor is introduced in the plane symmetric metric in such a way so as to obtain the same number of Noether symmetries as for the exact plane symmetric spacetime. The corresponding approximate conservation is obtained to discuss the conservation laws of the energy and momentum during the formation of gravitational wave.

In this short paper, we discuss the possibility of testing the nature of astrophysical black holes using the recently observed black hole mergers. We investigate the possibility that a secondary black hole is created in the merger of two astrophysical black holes and discuss potential astrophysical signatures. We point out that black hole mergers are a possible astrophysical mechanism for the creation of quantum black holes with masses close to the Planck mass.