English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Utilizing various gauges of the radial coordinate, we give a GeneralRelativistic (GR) description of static spherically symmetric spacetimes with amassive point source and vacuum outside this singularity. We show that in GRthere exists a two-parameter family of such solutions to the Einstein equationswhich are physically distinguishable and describe the gravitational field of asingle massive point particle with positive proper mass $M_0$ and positiveKeplerian mass $M<M_0$. In particular, we show that the widespread Hilbert formof the Schwarzschild solution, which depends only on the Keplerian mass $M$ anddescribes Black Holes (BH), does not solve the Einstein equations with amassive point particle stress-energy tensor. Novel normal coordinates for thegravitational field and a new physical class of gauges are proposed, thusachieving a correct description of a point mass source in GR. We also introducea gravitational mass defect of a point particle and determine the dependence ofthe solutions on this mass defect. The result can be described as a change ofthe Newton potential $\varphi_{\!{}_N}=-G_{\!{}_N}M/r$ to a modified one$\varphi_{\!{}_G}=-G_{\!{}_N}M/ \left(r+G_{\!{}_N} M/c^2\ln{{M_0}\overM}\right)$ and the corresponding modification of the four-interval. We showthat the proper 3D flat space, where these two potentials can be compared, isthe tangent space above the position of the massive point source. In addition,we present invariant characteristics of the physically and geometricallydifferent classes of spherically symmetric static spacetimes created by a pointmass. Our findings are important for description of Extremely Compact Objects(ECOs) studied in relation with possible echoes in Gravitational Waves (GW)recently discovered by the LIGO/VIRGO collaboration. %

The Era of Gravitational Astronomy and Gravitational Field of Non-Rotating Single Point Particle in General Relativity