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It seems to me that once black holes were theorised then the obvious singularity at its centre - though only ratified after Hawking and Penrose's singularity theorems - one would have to ask where the matter and energy went to, if we are to save the conservation of mass-energy. After Einstein & Rosen theorised the Einstein-Rosen Bridge, the otherwise known, wormhole, the obverse of a black hole could be thought: that is a white hole. Here, matter or light can't enter it, but they can escape.

Was this the earliest conceptualisation of such, or was there an earlier conceptualisation? There's very little history about this in the usual sources.

**@Ben Crowell: Although I dreamt up the question, I don't think of it as a 'nice' question as its a little too simple-minded for that. It's no mistake on my part, as I'm referring to the original notion of a black hole by John Michell in the late 19th C though he called them dark stars. And the insight that gravity would produce a singularity was the insight of Roger Boscovitch if there was no countervailing pressure - though for him - this led to the notion of atoms and interatomic forces that push back against gravity in order that matter is stable - and this was well before atoms became fashionable.

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This is a nice question. As a preliminary, it contains a couple of physics mistakes.

It seems to me that once black holes were theorised then the obvious singularity at its centre

The singularity of a black hole is not a point at its center, it's a spacelike singularity.

one would have to ask where the matter and energy went to, if we are to save the conservation of mass-energy

Conservation of mass-energy is not a principle that can be formulated in GR for all spacetimes, although for black hole spacetimes it can be, because they're asymptotically flat. There is no difficulty with explaining where the mass-energy ends up. Given any event P, a spacelike surface can be constructed that includes P and that intersects the world-line of all infalling matter.

The Penrose singularity theorem is not particularly relevant. White holes are not expected to form as the result of gravitational collapse, for reasons independent of the reasons that originally led people to disbelieve the formation of black holes by gravitational collapse, until the Penrose singularity theorem.

So anyway, about the history: --

Finkelstein proposed the one-way membrane interpretation of the Schwarzschild spacetime in a 1958 paper. In the same paper, he references a communication from Kruskal describing the maximal extension of this spacetime, which includes a region referred to as region IV or, later, the "white hole" region.

The name "black hole" was probably current among some relativists as early as the early 60's (Herdeiro and Lemos), but was popularized in a lecture by Wheeler in 1967, which was published in written form in 1968. A google ngrams search shows that both "black hole" and "white hole" start to rise above background noise around 1968. Although it was clear immediately that white holes should not arise as the result of gravitational collapse, and were not expected to exist as astronomical objects, people did publish speculative/flaky ideas to the contrary as early as 1971. Examples are Robert Hjellming in 1971 and Narlikar in 1975.

So the conceptual apparatus of black holes and white holes appeared at the same time, in 1958, and both words began appearing in print at the same time, around 1968.

References

Finkelstein, Phys. Rev. 110, 965–967 (1958), "Past-Future Asymmetry of the Gravitational Field of a Point Particle," downloadable from his web page at https://www.physics.gatech.edu/user/david-finkelstein

Herdeiro and Lemos, https://arxiv.org/abs/1811.06587

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